Path Integrals In Quantum Mechanics, Statistics, And Polymer Physics (2nd Edition) - Hardcover

Kleinert, Hagen

Hardcover

ISBN 10: 9810214715 ISBN 13: 9789810214715

Publisher: World Scientific Publishing Co Pte Ltd, 1995

Synopsis

This is the second, significantly expanded edition of the comprehensive textbook of 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular of the hydrogen atom. The solutions have been made possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular 1/r- and 1/r2-potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion.The powerful Feynman-Kleinert variational approach is explained and developed systematically into a variational perturbation expansion. In contrast to ordinary perturbation expansions, divergencies are absent. Instead, there is a uniform convergence from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals.Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory now also applies to small orders.Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern-Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect.

About this title

Review

"Kleinert's book presents the reader with a very complete and very thorough discussion of path integration... a new extensive and, again, rather complete chapter has been added on the use of path integration techniques in the analysis of financial markets. This chapter would do well in any high-level course on stochastic financial models and is a wonderful occasion for candidate mathematical and theoretical physicists to realize what great potential there hides still in the methodologies and techniques that have been developed... It profits from the clarity and conciseness that is also a hallmark of Kleinert's scientific papers... this volume is highly recommendable for any student considering majoring in theoretical physics or chemistry, and an absolute must for any lecturer in this area... In fact, I don't know of any excuse not to have your own copy." Journal of Statistical Physics, Apr 2003"

Synopsis

This textbook on the theory and applications of path integrals contains the solution to a number of non-trivial path integrals, most notably that of the Coulomb system. This has become possible by finding a consistent formulation of path integrals in spaces with curvature and torsion. Special emphasis is given to stability problems of path fluctuations in the presence of singular potentials such as centrifugal and angular barriers. The limitations of Feynman's time slicing procedure are exhibited and a new path integral formula is found which avoids the frequent danger of path collapse. The physically important applications to tunnelling problems are analyzed in detail. Their relevance to superconductivity and the large-order behaviour of perturbation expansions is demonstrated. The path integral description of equilibrium thermodynamics is presented, and an extension to non-equilibrium processes is presented. Much attention is paid to path integrals in spaces with topological restrictions. Their applications to entanglement problems in polymer physics and their relevance to particle statistics are discussed, also to the recently popular phenomenon of fractional statistics.

Now in its second edition, the book has been extended by a more powerful variational approach which can now be applied to excited states and to tunnelling processes through high as well as low barriers. With it, the known large-order perturbation theory has been continued down to small orders. The book contains a detailed non-abelian Chern-Simons theory of polymer entanglement in terms of HOMFLY-polynomials and a discussion of anyonic aspects of the fractional quantum Hall effect and of high-Tc superconductivity. The semiclassical analysis incorporates now multidimensional systems to establish contact with recent work on chaos.

Edition details

• Publisher: World Scientific Publishing Co Pte Ltd
• Publication date: 1995
• ISBN 10: 9810214715
• ISBN 13: 9789810214715
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 920